Geometry 1-6 Complete Lesson: Basic Constructions

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Solve It!
How is segment GJ related to ∠FGH? How do you know?

Upload a picture of the paper you created for the Solve It! to the canvas.

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Take Note: Define geometric construction.

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Problem 1 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

G.CO.12

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Problem 2 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

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Take Note: Define perpendicular lines.

Sketch and label an example pair of perpendicular lines on the canvas.

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Problem 3 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

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Problem 4 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

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Digital Construction: Complete the following steps on the Geogebra Geometry Calculator above or at geogebra.org/geometry.

1. Construct segment PQ. Be sure to rename one endpoint P and the other Q and show the names.
2. Use the compass tool from the circle menu, followed by the segment tool once more, to construct a second segment, congruent to segment PQ.
3. Screenshot your work and upload it to the canvas.

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Digital Construction: Complete the following steps on the Geogebra Geometry Calculator above or at geogebra.org/geometry.

1. Construct segment PQ. Make sure that endpoint labels are shown and correct.
2. Use the compass and segment tools to construct a perpendicular bisector of segment PQ.
3. Screenshot your work and upload it to the canvas.

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Digital Construction: Complete the following steps on the Geogebra Geometry Calculator above or at geogebra.org/geometry.

1. Construct an obtuse ∠JKL.
2. Use the compass and segment tools to construct the angle bisector of ∠JKL.
3. Screenshot your work and upload it to the canvas.

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Compare and Contrast: Describe the difference in accuracy between sketching a figure, drawing a figure with a ruler and protractor, and constructing a figure. Explain.

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Error Analysis: Your friend constructs line XY so that it is perpendicular to and contains the midpoint of segment AB. He claims that segment AB is the perpendicular bisector of line XY. What is his error?

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Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

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Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

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Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

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Draggable item		Corresponding Item

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G.CO.12

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Reflection: Math Success

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Draggable item		Corresponding Item
ray
congruent
intersection of segments
point
vertex

Geometry 1-6 Complete Lesson: Basic Constructions

Solve It!How is segment GJ related to ∠FGH? How do you know?Upload a picture of the paper you created for the Solve It! to the canvas.

Take Note: Define geometric construction.

Problem 1 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 2 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Take Note: Define perpendicular lines.Sketch and label an example pair of perpendicular lines on the canvas.

Problem 3 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 4 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Digital Construction: Complete the following steps on the Geogebra Geometry Calculator above or at geogebra.org/geometry.1. Construct an obtuse ∠JKL.2. Use the compass and segment tools to construct the angle bisector of ∠JKL.3. Screenshot your work and upload it to the canvas.

Compare and Contrast: Describe the difference in accuracy between sketching a figure, drawing a figure with a ruler and protractor, and constructing a figure. Explain.

Error Analysis: Your friend constructs line XY so that it is perpendicular to and contains the midpoint of segment AB. He claims that segment AB is the perpendicular bisector of line XY. What is his error?

Algebra: Evaluate the expression for a = 6 and b = -8.Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.Enter only a number.

Reflection: Math Success

Solve It!How is segment GJ related to ∠FGH? How do you know?Upload a picture of the paper you created for the Solve It! to the canvas.

Take Note: Define geometric construction.

Take Note: What tools are allowed in geometric construction?

Problem 1 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 2 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Reasoning: How is constructing a congruent angle similar to constructing a congruent segment?

Take Note: Define perpendicular lines.Sketch and label an example pair of perpendicular lines on the canvas.

Take Note: Define perpendicular bisector.Sketch and label an example of a line segment and a perpendicular bisector on the canvas.

Problem 3 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 4 Got It?Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Digital Construction: Complete the following steps on the Geogebra Geometry Calculator above or at geogebra.org/geometry.1. Construct an obtuse ∠JKL.2. Use the compass and segment tools to construct the angle bisector of ∠JKL.3. Screenshot your work and upload it to the canvas.

Vocabulary: What two tools do you use to make constructions?

Compare and Contrast: Describe the difference in accuracy between sketching a figure, drawing a figure with a ruler and protractor, and constructing a figure. Explain.

Error Analysis: Your friend constructs line XY so that it is perpendicular to and contains the midpoint of segment AB. He claims that segment AB is the perpendicular bisector of line XY. What is his error?

Algebra: Evaluate the expression for a = 6 and b = -8.Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.Enter only a number.

Vocabulary Review: Match each term or set of terms on the left with the image that best represents it.

Use Your Vocabulary: Identify the figure that shows perpendicular segments.

Use Your Vocabulary: Identify the figure that shows the perpendicular bisector of a segment.

Tool Selection: Which tool is used to complete the task?measure lines

Tool Selection: Which tool is used to complete the task?measure angles

Tool Selection: Which tool is used to complete the task?construct arcs

Tool Selection: Which tool is used to complete the task?construct lines

Reflection: Math Success

Take Note: What tools are allowed in geometric construction?

Reasoning: How is constructing a congruent angle similar to constructing a congruent segment?

Take Note: Define perpendicular bisector.Sketch and label an example of a line segment and a perpendicular bisector on the canvas.

Solve It!
How is segment GJ related to ∠FGH? How do you know?

Upload a picture of the paper you created for the Solve It! to the canvas.

Problem 1 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 2 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Take Note: Define perpendicular lines.

Sketch and label an example pair of perpendicular lines on the canvas.

Problem 3 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 4 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Digital Construction: Complete the following steps on the Geogebra Geometry Calculator above or at geogebra.org/geometry.

1. Construct an obtuse ∠JKL.
2. Use the compass and segment tools to construct the angle bisector of ∠JKL.
3. Screenshot your work and upload it to the canvas.

Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

Solve It!
How is segment GJ related to ∠FGH? How do you know?

Upload a picture of the paper you created for the Solve It! to the canvas.

Problem 1 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 2 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Take Note: Define perpendicular lines.

Sketch and label an example pair of perpendicular lines on the canvas.

Take Note: Define perpendicular bisector.

Sketch and label an example of a line segment and a perpendicular bisector on the canvas.

Problem 3 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Problem 4 Got It?
Complete your construction on paper with a compass and straightedge, take a picture of your work, then add your image to the canvas.

Digital Construction: Complete the following steps on the Geogebra Geometry Calculator above or at geogebra.org/geometry.

1. Construct an obtuse ∠JKL.
2. Use the compass and segment tools to construct the angle bisector of ∠JKL.
3. Screenshot your work and upload it to the canvas.

Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

Algebra: Evaluate the expression for a = 6 and b = -8.
Enter only a number.

Tool Selection: Which tool is used to complete the task?

measure lines

Tool Selection: Which tool is used to complete the task?

measure angles

Tool Selection: Which tool is used to complete the task?

construct arcs

Tool Selection: Which tool is used to complete the task?

construct lines

Take Note: Define perpendicular bisector.

Sketch and label an example of a line segment and a perpendicular bisector on the canvas.